In General Touch Bar Settings:
Unchecking "Hide global actions if app specific actions are configured in BTT" makes a dropdown menu appear, giving me the choice to "Show global actions before/after App Specific actions".
Surely, that must be a mistake since I just decided not to show them? Also, whichever I choose in that dropdown, the global actions seem to be un-invokable.
Device information:
if you uncheck the hide option, the global ones will also be shown when app-specific have been configured. Therefore you can change the order only then.
I am stupid of course — I meant to write CHECKING, not unchecking. 
So rather: checking HIDE did indeed (previously) produce that dropdown menu, which no doubt must have been unexpected behavior.
Just wanted to clarify — because anyway, this was before updating to 2.687. Now that I have, neither checking nor unchecking that box seems to give me a dropdown menu.
you were right about that issue 
The dropdown has been replaced with the more powerful ability to set a display order value for every Touch Bar button / widget in BTT.